Let put some answers to this. Otherwise we will forever have only the question. This is my understanding:
Atta = self (oneself, himself, yourself); soul (in a Sanskrit sense); [atthaa = self-interest; อัตถา = เห็น แก่/แต่ ตัว]
anatta = an (not, no/without) negation prefix + atta (as above) = not self, not oneself = noneself; without soul; [my comment: this is not the same 'nothing' (สุญญตา = emptiness -- in material or mental sense)]
From A Pali-English dictionary, we see some differences in Thai and Pali (and Sanskrit) meanings (Thai 'atta' = ตัวตน in the sense Id/Ego and so 'annata' = "ไม่มี" ตัวตน or "ไม่ใช่" ตัวตน or perhaps "ไม่เป็น" ตัวตน).
The concept of 'self' as an entity separate-able from its environment (not self) underlines a subtle meaning of atta and its negation or 'complement' (for those Set Theorists). If we can clearly describe what is 'self', then anything else is 'not self'. Alternatively, we can clearly describe 'not self', then anything else is 'not not-self' (='self'?). Is อัตตะ 'atta' the same as สติ 'sati' or self-awareness or self-consciousness? ...
To cut some tanglements, we can take a meaning of 'atta' as just 'oneself' in a possessive sense. 'Annata' then means 'not self in possessive sense. Here we cover 'กู ตัว(ของ)กู ของกู' and any generalization of กู (myself) to 'มึง ตัว(ของ)มึง ของมึง', 'เขา ตัว(ของ)เขา ของเขา' or 'oneself'; and come to the problem of 'an-' as negation or complement. From a Buddhist point of view, 'detachment' is a principle concept and an aim of practice (nibbaana is complete detachment), buddhist should train to understand 'self' and to become 'undetached' to 'self'. [Somehow this and other stories in the Tipitaka suggest 'focus on self' (not other ir-relevant outside) to lose focus on self'. Maybe because we can know about ourselves better than 'not ourselves'.]
The Buddha asked in a Tipitaka story: 'Monks, are there more leaves in my hand or out of my hand?'
OK. Your turn ;-)